Liquid dispenser systems, such as liquid soap and sanitizer dispensers, provide a user with an amount of foam upon actuation of the dispenser. In order to create a foam output having a desirable characteristic, the air to liquid ratio is generally about 10 to 1. To accomplish this, most prior art foam pumps have an air pump chamber that has an outside diameter that is larger than the interior diameter of the neck of the container. Consequently, the air pump chamber is typically located outside of the neck of the container. Locating the air pump chamber outside of the container increases the overall size of the refill and increases the shipping costs.